Permutation tests for nonparametric detection

In this paper, the authors provide a methodology to design nonparametric permutation tests and, in particular, nonparametric rank tests for applications in detection. In the first part of the paper, the authors develop the optimization theory of both permutation and rank tests in the Neyman?Pearson sense; in the second part of the paper, they carry out a comparative performance analysis of the permutation and rank tests (detectors) against the parametric ones in radar applications. First, a brief review of some contributions on nonparametric tests is realized. Then, the optimum permutation and rank tests are derived. Finally, a performance analysis is realized by Monte-Carlo simulations for the corresponding detectors, and the results are shown in curves of detection probability versus signal-to-noise rati

Deducing corticotropin-releasing hormone receptor type 1 signaling networks from gene expression data by usage of genetic algorithms and graphical Gaussian models

<p>Abstract</p> <p>Background</p> <p>Dysregulation of the hypothalamic-pituitary-adrenal (HPA) axis is a hallmark of complex and multifactorial psychiatric diseases such as anxiety and mood disorders. About 50-60% of patients with major depression show HPA axis dysfunction, i.e. hyperactivity and impaired negative feedback regulation. The neuropeptide corticotropin-releasing hormone (CRH) and its receptor type 1 (CRHR1) are key regulators of this neuroendocrine stress axis. Therefore, we analyzed CRH/CRHR1-dependent gene expression data obtained from the pituitary corticotrope cell line AtT-20, a well-established <it>in vitro </it>model for CRHR1-mediated signal transduction. To extract significantly regulated genes from a genome-wide microarray data set and to deduce underlying CRHR1-dependent signaling networks, we combined supervised and unsupervised algorithms.</p> <p>Results</p> <p>We present an efficient variable selection strategy by consecutively applying univariate as well as multivariate methods followed by graphical models. First, feature preselection was used to exclude genes not differentially regulated over time from the dataset. For multivariate variable selection a maximum likelihood (MLHD) discriminant function within GALGO, an R package based on a genetic algorithm (GA), was chosen. The topmost genes representing major nodes in the expression network were ranked to find highly separating candidate genes. By using groups of five genes (chromosome size) in the discriminant function and repeating the genetic algorithm separately four times we found eleven genes occurring at least in three of the top ranked result lists of the four repetitions. In addition, we compared the results of GA/MLHD with the alternative optimization algorithms greedy selection and simulated annealing as well as with the state-of-the-art method random forest. In every case we obtained a clear overlap of the selected genes independently confirming the results of MLHD in combination with a genetic algorithm.</p> <p>With two unsupervised algorithms, principal component analysis and graphical Gaussian models, putative interactions of the candidate genes were determined and reconstructed by literature mining. Differential regulation of six candidate genes was validated by qRT-PCR.</p> <p>Conclusions</p> <p>The combination of supervised and unsupervised algorithms in this study allowed extracting a small subset of meaningful candidate genes from the genome-wide expression data set. Thereby, variable selection using different optimization algorithms based on linear classifiers as well as the nonlinear random forest method resulted in congruent candidate genes. The calculated interacting network connecting these new target genes was bioinformatically mapped to known CRHR1-dependent signaling pathways. Additionally, the differential expression of the identified target genes was confirmed experimentally.</p

Dissection of Complex Genetic Correlations into Interaction Effects

Living systems are overwhelmingly complex and consist of many interacting parts. Already the quantitative characterization of a single human cell type on genetic level requires at least the measurement of 20000 gene expressions. It remains a big challenge for theoretical approaches to discover patterns in these signals that represent specific interactions in such systems. A major problem is that available standard procedures summarize gene expressions in a hard-to-interpret way. For example, principal components represent axes of maximal variance in the gene vector space and thus often correspond to a superposition of multiple different gene regulation effects (e.g. I.1.4). Here, a novel approach to analyze and interpret such complex data is developed (Chapter II). It is based on an extremum principle that identifies an axis in the gene vector space to which as many as possible samples are correlated as highly as possible (II.3). This axis is maximally specific and thus most probably corresponds to exactly one gene regulation effect, making it considerably easier to interpret than principle components. To stabilize and optimize effect discovery, axes in the sample vector space are identified simultaneously. Genes and samples are always handled symmetrically by the algorithm. While sufficient for effect discovery, effect axes can only linearly approximate regulation laws. To represent a broader class of nonlinear regulations, including saturation effects or activity thresholds (e.g. II.1.1.2), a bimonotonic effect model is defined (II.2.1.2). A corresponding regression is realized that is monotonic over projections of samples (or genes) onto discovered gene (or sample) axes. Resulting effect curves can approximate regulation laws precisely (II.4.1). This enables the dissection of exclusively the discovered effect from the signal (II.4.2). Signal parts from other potentially overlapping effects remain untouched. This continues iteratively. In this way, the high-dimensional initial signal (II.2.1.1) can be dissected into highly specific effects. Method validation demonstrates that superposed effects of various size, shape and signal strength can be dissected reliably (II.6.2). Simulated laws of regulation are reconstructed with high correlation. Detection limits, e.g. for signal strength or for missing values, lie above practical requirements (II.6.4). The novel approach is systematically compared with standard procedures such as principal component analysis. Signal dissection is shown to have clear advantages, especially for many overlapping effects of comparable size (II.6.3). An ideal test field for such approaches is cancer cells, as they may be driven by multiple overlapping gene regulation networks that are largely unknown. Additionally, quantification and classification of cancer cells by their particular set of driving gene regulations is a prerequisite towards precision medicine. To validate the novel method against real biological data, it is applied to gene expressions of over 1000 tumor samples from Diffuse Large B-Cell Lymphoma (DLBCL) patients (Chapter III). Two already known subtypes of this disease (cf. I.1.2.1) with significantly different survival following the same chemotherapy were originally also discovered as a gene expression effect. These subtypes can only be precisely determined by this effect on molecular level. Such previous results offer a possibility for method validation and indeed, this effect has been unsupervisedly rediscovered (III.3.2.2). Several additional biologically relevant effects have been discovered and validated across four patient cohorts. Multivariate analyses (III.2) identify combinations of validated effects that can predict significant differences in patient survival. One novel effect possesses an even higher predictive value (cf. III.2.5.1) than the rediscovered subtype effect and is genetically more specific (cf. III.3.3.1). A trained and validated Cox survival model (III.2.5) can predict significant survival differences within known DLBCL subtypes (III.2.5.6), demonstrating that they are genetically heterogeneous as well. Detailed biostatistical evaluations of all survival effects (III.3.3) may help to clarify the molecular pathogenesis of DLBCL. Furthermore, the applicability of signal dissection is not limited to biological data. For instance, dissecting spectral energy distributions of stars observed in astrophysics might be useful to discover laws of light emission